共查询到20条相似文献,搜索用时 11 毫秒
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《Computers & Mathematics with Applications》2005,49(5-6):943-952
Using the technique associated with measures of noncompactness we prove the existence of monotonic solutions of a class of quadratic integral equation of Volterra type in the Banach space of real functions defined and continuous on a bounded and closed interval. 相似文献
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M. Muslim Carlos Conca A.K. Nandakumaran 《Computers & Mathematics with Applications》2010,59(3):1236-1244
In this paper we shall study a fractional integral equation in an arbitrary Banach space . We used the analytic semigroups theory of linear operators and the fixed point method to establish the existence and uniqueness of solutions of the given problem. We also prove the existence of global solution. The existence and convergence of the Faedo–Galerkin solution to the given problem is also proved in a separable Hilbert space with some additional assumptions on the operator . Finally we give an example to illustrate the applications of the abstract results. 相似文献
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A nonlinear stochastic integral equation of the Hammerstein type in the formx(t; ) = h(t, x(t; )) +
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k(t, s; )f(s, x(s; ); )d(s) is studied wheret S, a measure space with certain properties, , the supporting set of a probability measure space (,A, P), and the integral is a Bochner integral. A random solution of the equation is defined to be an almost surely continuousm-dimensional vector-valued stochastic process onS which is bounded with probability one for eacht S and which satisfies the equation almost surely. Several theorems are proved which give conditions such that a unique random solution exists.
AMS (MOS) subject classifications (1970): Primary; 60H20, 45G99. Secondary: 60G99. 相似文献
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W. A. Coppel 《Systems & Control Letters》1983,3(2):117-118
We derive a number of properties of a new type of matrix quadratic equation, including the existence of a maximal solution. 相似文献
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In this paper, we consider the discrete Legendre spectral Galerkin method to approximate the solution of Urysohn integral equation with smooth kernel. The convergence of the approximate and iterated approximate solutions to the actual solution is discussed and the rates of convergence are obtained. In particular we have shown that, when the quadrature rule is of certain degree of precision, the superconvergence rates for the iterated Legendre spectral Galerkin method are maintained in the discrete case. 相似文献
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《Computers & Mathematics with Applications》2001,41(7-8):835-842
We consider the existence of positive solutions to the nonlinear integral equation where g is a continuous, nondecreasing function such that g(0) = 0. We show that the equation always has nontrivial solutions and we give a necessary and sufficient condition for the existence of solutions u such that u(x) > − ∞. We also provide a condition which ensures that all the nontrivial solutions experience the blow-up behaviour. 相似文献
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The object of the paper is concerned with the existence and uniqueness of a random solution, a second-order stochastic process, of a non-linear perturbed random integral equation of the formx where tεR+ and coωεΩ, the supporting set of a probability measure space (Ω,A,μ). Several Jianach spaces and Bunnell's fixed point theorem are the primary techniques used. 相似文献
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In this paper, we investigate a nonlinear Urysohn integral equation on unboundedinterval. We show that under some assumptions that the equation has monotonic solutions belonging to the space of functions being Lebesgue integrable on unbounded interval. The main tool used in our study is the technique associated with measures of weak noncompactness and measures of noncompactness in strong sense. 相似文献
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One of the author's favorite experiences in high school mathematics was learning how to solve quadratic equations. As is usual with life, things are not as simple as they were in high school. There are several problems with the quadratic formula. In this article, the author talks about these problems and various solutions to them. 相似文献
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W. J. Padgett 《Theory of Computing Systems》1973,7(2):164-169
Summary Tsokos [12] showed the existence of a unique random solution of the random Volterra integral equation (*)x(t; ) = h(t; ) +
o
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k(t, ; )f(, x(; )) d, where , the supporting set of a probability measure space (,A, P). It was required thatf must satisfy a Lipschitz condition in a certain subset of a Banach space. By using an extension of Banach's contraction-mapping principle, it is shown here that a unique random solution of (*) exists whenf is (, )-uniformly locally Lipschitz in the same subset of the Banach space considered in [12]. 相似文献
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《国际计算机数学杂志》2012,89(5):957-968
In this paper, by using the integral bifurcation method, we study a nonlinear dispersive equation. Some new soliton-like solutions and some compacton-like periodic wave solutions are obtained. Their dynamic characters are investigated and the profiles are given by the mathematical software Maple. From the graphs of some soliton-like solutions, we find that their profiles are transformable. 相似文献
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System analysis via integral quadratic constraints 总被引:1,自引:0,他引:1
This paper introduces a unified approach to robustness analysis with respect to nonlinearities, time variations, and uncertain parameters. From an original idea by Yakubovich (1967), the approach has been developed under a combination of influences from the Western and Russian traditions of control theory. It is shown how a complex system can be described, using integral quadratic constraints (IQC) for its elementary components. A stability theorem for systems described by IQCs is presented that covers classical passivity/dissipativity arguments but simplifies the use of multipliers and the treatment of causality. A systematic computational approach is described, and relations to other methods of stability analysis are discussed. Last, but not least, the paper contains a summarizing list of IQCs for important types of system components 相似文献
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The need for providing reliable numerical methods for the solution of weakly singular Volterra integral equations ofI st Kind stems from the fact that they are connected to important problems in the theory and applications of stochastic processes. In the first section are briefly sketched the above problems and some peculiarities of such equations. Section 2 described the method for obtaining an approximate solution whose properties are described in section 3: such properties guarantee that our approximate solution always oscillates around the rigorous one. Section 4 discusses the applicability to our case of some classical bounds on the errors. The remaining sections are all devoted to the construction of upper bounds on the oscillating error in order to reach a high degree of reliability for our solution. All the bounds are independent on the numerical method which is employed for obtaining the numerical solution. In section 5 is derived a Volterra II Kind integral equation by subtracting to the original kernel the weak singularity, while in section 6 is given an upper bound to the error in the case of Wiener and Ornstein-Ühlenbeck kernels with constant barriers. Such a bound is generalized to other kinds of barriers in section 7 while in section 8 is suggested an approximation of the Kernel for the O. Ü. case with constant barriers and by means of it is given an explicit bound for the error in terms of Abel's transform of the known term in the original integral equation. A rough estimation of the error is also given under the assumption that \(y(t) - \int\limits_0^t {K(t,\tau )\tilde x(\tau )d_\tau [\tilde x(\tau )} \) denotes any approximate solution of (1a) obtained by any method] can be approximated by means of a sinusoidal function. In section 9 is derived another kind of bound, for constant barriers, by using the approximate Kernel of section 7 and classical results. 相似文献
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那顺布和 《动力学与控制学报》2010,8(2):119-122
在Kondratiev分布空间(S)-1中通过埃尔米特变换和Painleve′分析导出了Wick-类型的随机广义Kdv方程的Backlund变换,并且把Wick-类型的随机广义Kdv方程变成广义系数Kdv-方程,再利用Backlund变换求出广义系数Kdv方程的精确解,最后通过埃尔米特逆变换求出随机广义Kdv方程在系数取不同白色噪音泛函条件下的精确解. 相似文献
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We derived an algorithm to find the real roots of the homogeneous quadratic equation, Ax/sup 2/+2Bxw+Cw/sup 2/=0. Because the equation is homogeneous, a root consists of an [x, w] pair where any nonzero multiple represents the same root. We strove to find an algorithm that didn't blow up no matter what values of A, B, and C we were given, including various combinations of zeroes. At the end of the article the author wrote the final algorithm in tabular form. 相似文献